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Magnetic Tracker with High Precision
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 25 (2011) 1617 – 1620 www.elsevier.com/locate/procedia
Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece
Magnetic tracker with high precision P.Ripka, A.Zikmund Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Measurement, Czech Republic, Prague
Abstract 3-D magnetic tracker working at very low frequency was developed to measure distances up to 1 m. The uncertainty caused by noise and interference is below 1 mm even in the noisy environment. The measurement time of 3 minutes can be decreased to 1 s depending on the amplitude of interferences and required accuracy. Systematic errors of ±1 cm can be corrected by using calibration model.
© 2011 Published by Elsevier Ltd. Keywords: magnetic distance sensor;magnetic tracker
1. Introduction In [1] we described implantable magnetic distance measurement system for the stomach volume estimation. The system is based on 2 mm diameter transmission and detection coils and it was working at 3 kHz frequency. Basic accuracy was 1 mm at 5 cm distance and 5 mm at 10 cm distance. The main source of error was angular mismatch and lateral displacement between the coils. In single-source, singlesensor system these effects cannot be corrected and they can cause gross errors: in extreme case (when the angular mismatch is 90°) the signal is completely lost. In order to reduce this error below 10 % for any angular position we employed 3-axial detection coil [2]. Similar system using AMR sensors was described in [3]. In this paper we show an industrial type of a magnetic tracker which works for distances up to 1 m. The main application is precise measurement of distances without direct sight. In building industry and archeology this is most often measurement of the wall thickness. In the mining industry the requirement is to measure the distance between two drills for explosives. These holes are drilled in parallel, but in reality they are always inclined; the exact amount of explosive is calculated for each case from the measured distances. In these applications optical or ultrasonic systems cannot be used. RF methods also fail due to the presence of conductive objects.
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.12.400
1618 2
P. Ripka A. Zikmund / Procedia Engineering (2011) 1617 – 1620 Authorand name / Procedia Engineering 00 (2011)25000–000
1.1. 3-D magnetic tracking system Our system use triaxial field source and triaxial field sensor. Fig. 1 shows them in arbitrary position characterized by distance, elevation and azimuth and by roll, pitch and yaw of the sensor triplet. Repetitive current pulses of both polarities are sequentially sent to individual source coils U,V and W. The unknown distance and 5 angles can be calculated from the 9 measured field differences BXU, BXV, BXW, .... BZW. In our specific case we were concentrated on the evaluation of the distance and therefore in this paper we do not discuss the accuracy of the evaluation of position angles.
Fig. 1. Sketch of three source coils U, V and W and three magnetic sensors X, Y and Z
The instrument should work in the vicinity of highly conductive objects. In order to avoid field distortion by eddy currents we had to use a very low frequency – typically squarewave below 10 Hz. Using DC field (e.g. from permanent magnet) is not practical, as it cannot be distinguished from the Earth’s field. For such low frequencies induction coil of required sensitivity would be too big and heavy. AMR sensors have noise level of 5 nT, which is too high for required accuracy. Therefore we used 3axial fluxgate sensor (Billingsley TFM100G2). The magnetic field of small solenoid coil in the distance of r larger than the coil size can be approximated by the formula for ideal dipole with magnetic moment of m = NIS The radial component of the generated magnetic field is Br = 20mcos/4r3 = cos· 2 · 4 · 10-7 NIS/4r3 = cos· 2NIS x 10-7/r3 (T) = cos· 200 NIS/r3 (nT) and the tangential component is: B = 0msin/4r3 where is the angle between the coil axis and r the direction to the measured point.Our source coils are 35 mm long, 22/35 mm diameter 300-turn solenoids mounted orthogonally. With 1.5 A current each of them has a dipole moment of 0.287 Am2. In the distance of 1 m the maximum theoretical field is 57 nT in the axial direction (in 1st Gauss position). If we commutate the current polarity, the field step is double, i.e. 114 nT. In the same distance the minimum field is 28 nT (in the 2nd Gauss position).
1619 3
P. RipkaAuthor and A. name Zikmund / Procedia Engineering 25 (2011) 1617 – 1620 / Procedia Engineering 00 (20111) 000–000
2. Measured values All Figs. 2 and 3 show the distance measurement in 1-D case: both source coil and sensor are positioned perfectly axially. Measured values (Fig. 2a) fit with the theoretical curve B~1/r3 for the ideal dipole source. Deviation from this rule is expected in the small distance where the size of the source coil cannot be neglected. For long distances the signal is very weak compared to the noise. Main noise sources are external environment (mainly electric currents and movement of ferromagnetic objects) and own noise of the sensor. In our case the sensor noise was in the range of 10 pT/Hz@1Hz, which was negligible compared to the environmental noise. Fig. 2b shows the resulting error: even for 4 cm distance the absolute error was below 1 mm. It should be noticed that in larger distances the measured field steps were extensively averaged to reduce the noise. 0,10 100000.0
measured
0,08
fitted 44.3/x^3
0,06 Error (cm )
Bx (nT)
10000.0
1000.0
0,04 0,02 0,00 -0,02
100.0
0
0,2
0,4
0,6
0,8
-0,04 -0,06
10.0 0
0.2
0.4
0.6
0.8
Distance (m)
1 1.2 Distance (m)
Fig. 2. (a) Axial field as a function of distance. The dipole moment of the source was 0.3522 Am2; (b) Error in the distance estimation for 1-axial case, building environment, measurement 3 minutes.
Situation for arbitrary 3-D position is much more complicated. In the Fig. 3 we show the signals in 0.5 m distance when the sensor head is rotated in the horizontal plane. From similar data the non-orthogonality of both source coils and magnetic sensors can be calculated. Exited by U coil
350
X sensor Y sensor Z sensor
250
250
50
50
45
90
135
180
225
270
315
360
B (nT)
150
B (nT)
150
-50 0
Exited by V coil
350
-50 0
-150
-150
-250
-250
45
90
135
180
225
360
Source rotation (deg)
Source rotation (deg)
(a)
315
X sensor Y sensor Z sensor
-350
-350
270
(b)
Fig. 3. Signals from U (a) and V (b) coils rotated in horizontal plane, the sensor head in 50 cm distance.
Fig. 4a shows the uncorrected error for the same experiment. The error curve with amplitude of ±12 mm has several components caused by imperfections of both the source coil and sensor system:
1620 4
P. Ripka A. Zikmund / Procedia Engineering (2011) 1617 – 1620 Authorand name / Procedia Engineering 00 (2011)25000–000
- differences of the coil dipole moments and sensor sensitivities - angular deviations or both triplets from the ortogonality - the triplets are not located in a single point - the rotation axis is not exactly in the center of all sensors The sensor offsets and their temperature drifts, which is normally the most severe problem of magnetic sensors, are suppressed by commutation of the source coil currents. The most significant error source is the fact that the individual coil centers are not located in the same point. This should be incorporated into the evaluation algorithm. The other imperfections contribute with max. 1% errors, which are acceptable without correction for many applications. The tracker will be used in the magnetically noisy environment. For typical 3-minutes data file containing 200 sets of 6 3-axial measurements (Fig. 4b), the RMS noise of the external field of 64, 98 and 389 nT in the X,Y and Z directions respectively was reduced to 1.5, 4.3 and 12.8 nT. The uncertainty can be further reduced below 1 nT by longer averaging. These are values typical for a city environment. The field variations in a rural area and in industrial environment may vary by an order of magnitude. 8,050
0.49
+W -W
Bx (nT)
0.485
8,000 7,975 7,950
0.48
-49,200 -49,400 Bz (nT)
0.475 0.47
-49,600 -49,800 -50,000 80
0.465 0.46 0
45
90
135
180
225
270
315 360 Source rotation (deg)
Bz difference (nT)
Estimated distance (m)
8,025
30 -20 -70 -120 0
(a)
20
40
60
80
100
120
140
time (s) 160
(b)
Fig. 1. (a) Magnetic field for +I and –I current into the W coil; (b) corresponding difference BZW
3. Conclusions The accuracy we are presently able to achieve is 3-times better than the system described in [4] which was using fusion of inertial and magnetic sensors. References [1] Tomek J, Mlejnek P, Janasek V, et al.: Gastric motility and volume sensing by implanted magnetic sensors, Sensor Letters 5 (2007), 276-278 [2] J. Tomek, P. Mlejnek, V. Janásek, P. Ripka, P. Kašpar and J. Chen: The precision of gastric motility and volume sensing by implanted magnetic sensors, Sensors and Actuators A 142 (2008), 34-39. [3] Liu Y., Y. Wang, D. Yan, Y. Zhou: DPSD Algorithm for AC Magnetic Tracking System, IEEE conf. Virtual Environments Human-Computer Interface and Meas. Syst., (2004), 101-106. [4] H. M. Schepers, D. Roetenberg, P. H. Veltink: Ambulatory human motion tracking by fusion of inertial and magnetic sensing with adaptive actuation, Med Biol Eng Comput (2010) 48:27–37
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 25 (2011) 1617 – 1620 www.elsevier.com/locate/procedia
Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece
Magnetic tracker with high precision P.Ripka, A.Zikmund Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Measurement, Czech Republic, Prague
Abstract 3-D magnetic tracker working at very low frequency was developed to measure distances up to 1 m. The uncertainty caused by noise and interference is below 1 mm even in the noisy environment. The measurement time of 3 minutes can be decreased to 1 s depending on the amplitude of interferences and required accuracy. Systematic errors of ±1 cm can be corrected by using calibration model.
© 2011 Published by Elsevier Ltd. Keywords: magnetic distance sensor;magnetic tracker
1. Introduction In [1] we described implantable magnetic distance measurement system for the stomach volume estimation. The system is based on 2 mm diameter transmission and detection coils and it was working at 3 kHz frequency. Basic accuracy was 1 mm at 5 cm distance and 5 mm at 10 cm distance. The main source of error was angular mismatch and lateral displacement between the coils. In single-source, singlesensor system these effects cannot be corrected and they can cause gross errors: in extreme case (when the angular mismatch is 90°) the signal is completely lost. In order to reduce this error below 10 % for any angular position we employed 3-axial detection coil [2]. Similar system using AMR sensors was described in [3]. In this paper we show an industrial type of a magnetic tracker which works for distances up to 1 m. The main application is precise measurement of distances without direct sight. In building industry and archeology this is most often measurement of the wall thickness. In the mining industry the requirement is to measure the distance between two drills for explosives. These holes are drilled in parallel, but in reality they are always inclined; the exact amount of explosive is calculated for each case from the measured distances. In these applications optical or ultrasonic systems cannot be used. RF methods also fail due to the presence of conductive objects.
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.12.400
1618 2
P. Ripka A. Zikmund / Procedia Engineering (2011) 1617 – 1620 Authorand name / Procedia Engineering 00 (2011)25000–000
1.1. 3-D magnetic tracking system Our system use triaxial field source and triaxial field sensor. Fig. 1 shows them in arbitrary position characterized by distance, elevation and azimuth and by roll, pitch and yaw of the sensor triplet. Repetitive current pulses of both polarities are sequentially sent to individual source coils U,V and W. The unknown distance and 5 angles can be calculated from the 9 measured field differences BXU, BXV, BXW, .... BZW. In our specific case we were concentrated on the evaluation of the distance and therefore in this paper we do not discuss the accuracy of the evaluation of position angles.
Fig. 1. Sketch of three source coils U, V and W and three magnetic sensors X, Y and Z
The instrument should work in the vicinity of highly conductive objects. In order to avoid field distortion by eddy currents we had to use a very low frequency – typically squarewave below 10 Hz. Using DC field (e.g. from permanent magnet) is not practical, as it cannot be distinguished from the Earth’s field. For such low frequencies induction coil of required sensitivity would be too big and heavy. AMR sensors have noise level of 5 nT, which is too high for required accuracy. Therefore we used 3axial fluxgate sensor (Billingsley TFM100G2). The magnetic field of small solenoid coil in the distance of r larger than the coil size can be approximated by the formula for ideal dipole with magnetic moment of m = NIS The radial component of the generated magnetic field is Br = 20mcos/4r3 = cos· 2 · 4 · 10-7 NIS/4r3 = cos· 2NIS x 10-7/r3 (T) = cos· 200 NIS/r3 (nT) and the tangential component is: B = 0msin/4r3 where is the angle between the coil axis and r the direction to the measured point.Our source coils are 35 mm long, 22/35 mm diameter 300-turn solenoids mounted orthogonally. With 1.5 A current each of them has a dipole moment of 0.287 Am2. In the distance of 1 m the maximum theoretical field is 57 nT in the axial direction (in 1st Gauss position). If we commutate the current polarity, the field step is double, i.e. 114 nT. In the same distance the minimum field is 28 nT (in the 2nd Gauss position).
1619 3
P. RipkaAuthor and A. name Zikmund / Procedia Engineering 25 (2011) 1617 – 1620 / Procedia Engineering 00 (20111) 000–000
2. Measured values All Figs. 2 and 3 show the distance measurement in 1-D case: both source coil and sensor are positioned perfectly axially. Measured values (Fig. 2a) fit with the theoretical curve B~1/r3 for the ideal dipole source. Deviation from this rule is expected in the small distance where the size of the source coil cannot be neglected. For long distances the signal is very weak compared to the noise. Main noise sources are external environment (mainly electric currents and movement of ferromagnetic objects) and own noise of the sensor. In our case the sensor noise was in the range of 10 pT/Hz@1Hz, which was negligible compared to the environmental noise. Fig. 2b shows the resulting error: even for 4 cm distance the absolute error was below 1 mm. It should be noticed that in larger distances the measured field steps were extensively averaged to reduce the noise. 0,10 100000.0
measured
0,08
fitted 44.3/x^3
0,06 Error (cm )
Bx (nT)
10000.0
1000.0
0,04 0,02 0,00 -0,02
100.0
0
0,2
0,4
0,6
0,8
-0,04 -0,06
10.0 0
0.2
0.4
0.6
0.8
Distance (m)
1 1.2 Distance (m)
Fig. 2. (a) Axial field as a function of distance. The dipole moment of the source was 0.3522 Am2; (b) Error in the distance estimation for 1-axial case, building environment, measurement 3 minutes.
Situation for arbitrary 3-D position is much more complicated. In the Fig. 3 we show the signals in 0.5 m distance when the sensor head is rotated in the horizontal plane. From similar data the non-orthogonality of both source coils and magnetic sensors can be calculated. Exited by U coil
350
X sensor Y sensor Z sensor
250
250
50
50
45
90
135
180
225
270
315
360
B (nT)
150
B (nT)
150
-50 0
Exited by V coil
350
-50 0
-150
-150
-250
-250
45
90
135
180
225
360
Source rotation (deg)
Source rotation (deg)
(a)
315
X sensor Y sensor Z sensor
-350
-350
270
(b)
Fig. 3. Signals from U (a) and V (b) coils rotated in horizontal plane, the sensor head in 50 cm distance.
Fig. 4a shows the uncorrected error for the same experiment. The error curve with amplitude of ±12 mm has several components caused by imperfections of both the source coil and sensor system:
1620 4
P. Ripka A. Zikmund / Procedia Engineering (2011) 1617 – 1620 Authorand name / Procedia Engineering 00 (2011)25000–000
- differences of the coil dipole moments and sensor sensitivities - angular deviations or both triplets from the ortogonality - the triplets are not located in a single point - the rotation axis is not exactly in the center of all sensors The sensor offsets and their temperature drifts, which is normally the most severe problem of magnetic sensors, are suppressed by commutation of the source coil currents. The most significant error source is the fact that the individual coil centers are not located in the same point. This should be incorporated into the evaluation algorithm. The other imperfections contribute with max. 1% errors, which are acceptable without correction for many applications. The tracker will be used in the magnetically noisy environment. For typical 3-minutes data file containing 200 sets of 6 3-axial measurements (Fig. 4b), the RMS noise of the external field of 64, 98 and 389 nT in the X,Y and Z directions respectively was reduced to 1.5, 4.3 and 12.8 nT. The uncertainty can be further reduced below 1 nT by longer averaging. These are values typical for a city environment. The field variations in a rural area and in industrial environment may vary by an order of magnitude. 8,050
0.49
+W -W
Bx (nT)
0.485
8,000 7,975 7,950
0.48
-49,200 -49,400 Bz (nT)
0.475 0.47
-49,600 -49,800 -50,000 80
0.465 0.46 0
45
90
135
180
225
270
315 360 Source rotation (deg)
Bz difference (nT)
Estimated distance (m)
8,025
30 -20 -70 -120 0
(a)
20
40
60
80
100
120
140
time (s) 160
(b)
Fig. 1. (a) Magnetic field for +I and –I current into the W coil; (b) corresponding difference BZW
3. Conclusions The accuracy we are presently able to achieve is 3-times better than the system described in [4] which was using fusion of inertial and magnetic sensors. References [1] Tomek J, Mlejnek P, Janasek V, et al.: Gastric motility and volume sensing by implanted magnetic sensors, Sensor Letters 5 (2007), 276-278 [2] J. Tomek, P. Mlejnek, V. Janásek, P. Ripka, P. Kašpar and J. Chen: The precision of gastric motility and volume sensing by implanted magnetic sensors, Sensors and Actuators A 142 (2008), 34-39. [3] Liu Y., Y. Wang, D. Yan, Y. Zhou: DPSD Algorithm for AC Magnetic Tracking System, IEEE conf. Virtual Environments Human-Computer Interface and Meas. Syst., (2004), 101-106. [4] H. M. Schepers, D. Roetenberg, P. H. Veltink: Ambulatory human motion tracking by fusion of inertial and magnetic sensing with adaptive actuation, Med Biol Eng Comput (2010) 48:27–37